Continuous Image of Connected Space is Connected/Corollary 1
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Corollary to Continuous Image of Connected Space is Connected
Connectedness is a topological property.
Proof
Follows directly from Continuous Image of Connected Space is Connected and the definition of topological property.
$\blacksquare$
Sources
- 1975: W.A. Sutherland: Introduction to Metric and Topological Spaces ... (previous) ... (next): $6.2$: Connectedness: Corollary $6.2.11$